Predicting the Oil Price Movement in Commodity Markets in Global Economic Meltdowns

forecasting
Article
Predicting the Oil Price Movement in Commodity Markets in
Global Economic Meltdowns
Jakub Horák * and Michaela Jannová

 Institute of Technology and Business in České Budějovice, School of Expertness and Valuation, Okružní 517/10,
 37001 České Budějovice, Czech Republic; michaelajannova@mail.vstecb.cz
 * Correspondence: horak@mail.vstecb.cz

 Abstract: The price of oil is nowadays a hot topic as it affects many areas of the world economy.
 The price of oil also plays an essential role in how the economic situation is currently developing
 (such as the COVID-19 pandemic, inflation and others) or the political situation in surrounding
 countries. The paper aims to predict the oil price movement in stock markets and to what extent the
 COVID-19 pandemic has affected stock markets. The experiment measures the price of oil from 2000
 to 2022. Time-series-smoothing techniques for calculating the results involve multilayer perceptron
 (MLP) networks and radial basis function (RBF) neural networks. Statistica 13 software, version 13.0
 forecasts the oil price movement. MLP networks deliver better performance than RBF networks and
 are applicable in practice. The results showed that the correlation coefficient values of all neural
 structures and data sets were higher than 0.973 in all cases, indicating only minimal differences
 between neural networks. Therefore, we must validate the prediction for the next 20 trading days.
 After the validation, the first neural network (10 MLP 1-18-1) closest to zero came out as the best.
 This network should be further trained on more data in the future, to refine the results.

 Keywords: oil; time series; gasoline; neural networks; prediction

 1. Introduction
 Oil prices require accurate predictions, given their imperativeness for the global econ-
Citation: Horák, J.; Jannová, M. omy [1]. Apart from fluctuating supply and demand, oil price movement reflects economic
Predicting the Oil Price Movement in development, financial markets, conflicts, wars and political issues [2]. Vochozka et al. [3]
Commodity Markets in Global
 argue that world oil prices spread into global economies, violently shaking macroeconomic
Economic Meltdowns. Forecasting
 dependent variables. Drebee and Razak [4] suggest that fluctuations in oil prices disrupt
2023, 5, 374–389. https://doi.org/
 economic growth. Khan et al. [5] pointed out the beneficial influence of global crises and
10.3390/forecast5020020
 the COVID-19 pandemic when investors start to speculate about the possible commodity
Academic Editor: Luigi Grossi price volatility, while Dai et al. [6] showed dramatic oil price changes during emergencies.
 Resource prices seriously harm the exchange rate [7]. Vochozka, Suler and Marousek [8]
Received: 6 February 2023
 suggest that the EUR/USD rate strongly depends on oil values, reflecting shifts in supply
Revised: 22 March 2023
Accepted: 23 March 2023
 and demand and global macroeconomic and geopolitical issues [9]. Supply and demand
Published: 27 March 2023
 and the investors’ sentiment chiefly factor into oil price movement [10].
 The mounting financial crisis has driven up oil and gas prices, indicating increases
 by dozens of percentage points compared with previous years. Gas prices have recently
 soared by dozens of crowns [11]. Many markets can readily adapt to rising costs but fail
Copyright: © 2023 by the authors. to conform when costs decrease [12]. Chen and Sun [13] revealed an asymmetry between
Licensee MDPI, Basel, Switzerland. gas prices in China and the global trend, indicating direct correspondence when the price
This article is an open access article soars but maladaptation in the event of a slump. Lv, Dong and Dong [14] found that oil
distributed under the terms and prices more profoundly affect stock returns in the sector of new energy vehicles than in
conditions of the Creative Commons
 other clean industries.
Attribution (CC BY) license (https://
 Xu et al. [15] suggest that the rise in gas prices should not shortly exceed 20%, to ensure
creativecommons.org/licenses/by/
 a stable consumer market. Valadkhani and Smyth [16] confirmed that while consumers feel
4.0/).

Forecasting 2023, 5, 374–389. https://doi.org/10.3390/forecast5020020 https://www.mdpi.com/journal/forecasting

Forecasting 2023, 5 375

 a slow and steady drop in commodity prices, their perception of the opposite is delayed
 but more intensive.
 The Czech Association of Petroleum Industry and Trade [17] predicts the highest
 demand for oil in the 2030s and 2040s.
 Fahmy [18] points to the growing interest in clean energy, which has profoundly
 impacted its price compared with oil prices and technological shares. Liden et al. [19] and
 Wang et al. [20] revealed that excessive oil and gas extraction has seriously polluted the
 environment. Mohamued et al. [21] proved an inverse relationship between oil prices and
 gas emissions in oil-exporting and -importing countries. The oil and gas sector has seen
 a tremendous improvement in oil and gas recycling. Although oil field development is
 costly, well-planned and advanced low-cost strategies will go a long way [22].
 The work aims to predict oil prices on stock markets, assessing the impact of the
 COVID-19 pandemic. Toward this aim, we formulated the following research questions:
 RQ1: What will be the oil and gas prices on the commodity market in November 2022?
 The global economies are always subject to change, intermittently experiencing fi-
 nancial crises (e.g., 1929, 2008) or worldwide epidemics such as the COVID-19 pandemic.
 The second research question focuses on measuring the pandemic’s impact on the price
 movements of the given resources.
 RQ2: What was the impact of the COVID-19 pandemic on oil stock prices?
 The article includes literary research with links to up-to-date scholarly literature, while
 the methods involve a regression analysis using neural networks evaluated in the Statistica
 program. The results contain our findings, a discussion of the research questions and a
 comparison of our results with those of other authors. The conclusion reviews the findings,
 giving practical recommendations.
 The paper refers to a very current topic addressing companies, researchers and gov-
 ernments. Nowadays, the price of oil, and subsequently the price of gasoline, is a highly
 discussed topic, especially with regard to the ongoing energy crisis, the war in Ukraine and
 instability in the world’s financial markets. This article uses the method of artificial neural
 networks, which is becoming more and more important in all possible problem-solving
 applications across all disciplines. The article is also unique in that it includes an authentic
 validation of the predicted oil price results. After further training the most successful neural
 networks for prediction, the selected networks can be applied to this issue in practice. An
 extensive sample of historical data is also used, which should ensure the relevance of the
 research. We are convinced that the results of this article will not only be beneficial to the
 academic community but also serve as a basis for further follow-up research, whose aim is
 to produce the most accurate prediction of oil prices in world markets.

 2. Literature Research
 Oil price movement calls for an accurate prediction, as it profoundly affects global
 economies [23,24]. In the field of energetics, researches have long discussed unstable oil
 prices in the stock market [25,26]. Qazi [27] found that oil price growth, triggered by global
 economy reinvigoration, hugely impacts the sentiment in the stock market. Low stock
 volatility and rising oil prices arouse rising expectations of money flows, whereas high
 fluctuations make markets focus on the crippling effects of enormous input costs.
 Singhal, Choudhary and Biswal [7] revealed that oil prices send unmistakable signals
 to monetary and fiscal policies, profoundly affecting stock markets and rates of exchange.
 We can predict the impacts of volatile oil prices on the EUR/USD exchange rate, improving
 corporate competitiveness in international markets [28]. Vrbka, Horák and Krulicky [29]
 explored the influence of oil price movement in the global market on Chinese currency by
 using neural networks. Although their results showed that fluctuating oil prices in stock
 markets somehow affect the CNY/USD exchange rate, they failed to gauge the extent.
 Vochozka, Horák and Krulicky [28] used an innovative neural network, long short-
 term memory (LSTM), for predicting oil prices, combining the created neural network
 with the integrated LSTM to forecast Brent oil prices. Herrera et al. [30] applied the same

Forecasting 2023, 5 376

 technique to explain the prices of oil, coal and gas. The RMSE and MAPE approaches
 measure the models’ accuracy, including an M-DM test for detecting statistically significant
 differences. The results show that machine-learning methods hugely outplay traditional
 econometric procedures, precisely identifying breakeven points.
 Khan et al. [5] used a dynamic simulation model for their experiment. They revealed
 that oil prices, the number of remittances and direct cross-border investments kickstart
 the stock market, whereas exchange rates have rather damaging effects. Zhao, Zhang and
 Wei [31] applied a recursive dynamic model of general equilibrium, exploring the impacts
 of rising and falling oil prices on investments and sectors of renewable energy resources.
 The authors found that rising oil prices may encourage investments in renewable energy,
 reduce the factual GNP and improve the environment, while the declining trend has had
 the opposite effect. Dabrowski et al. [32] used block-exogeneity panel vector autoregressive
 models to prove that shocks in oil prices and unsteady market trends seriously harm the
 respective economies of oil-exporting countries.
 Denghani and Zangeneh [33] proposed an alternative method, including biogeo-
 graphic optimization (BMMR-BBO), to estimate West Texas Intermediate’s oil prices, achiev-
 ing better outcomes than those of other techniques. Kumeka, Uzoma-Nwosu and David
 Wayas [34] used Granger causality, revealing that exchange rates may even stimulate the
 market, unlike what happened before the COVID-19 pandemic. On the other hand, the
 impulse response functions (IRFs) showed that oil price shocks provoked negative re-
 sponses in exchange rates only after the pandemic. Zafeirou et al. [35] found that high oil
 prices induced demand for agricultural products used for biodiesel and ethanol production,
 where energy and agricultural commodity markets closely interact.
 The presented studies suggest an avid global interest in the discussed topic, including
 many articles and innovative methods. However, the best techniques have yet to come.
 Scholars have also measured how oil prices shook stock markets or affected the environ-
 ment. Artificial neural networks involve the most applicable methods. We, therefore, use
 neural structures for predicting oil price movement in November 2022 (RQ1), while time
 series will be better at assessing whether the COVID-19 pandemic harmed or left intact the
 given commodity (RQ2).

 3. Materials and Methods
 We measure oil price movement from 2000 to 2022 and the associated emission limits
 and costs that companies incurred. Detecting the fuel prices at gas stations allows us to
 explore the driving forces behind the substantial fuel price rise, either out of necessity or
 out of a distributor’s tactics to exploit the situation.
 We collected the data from the macrotrends.net website access of 2 October 2022,
 disclosing oil prices on every negotiated day. Our study involved Brent oil prices (WTI)
 measured in barrel units, comprising daily data from the New York Stock Exchange (NYSE).
 The stock market uses two indexes, namely the NYSE Composite, covering all negotiated
 stock, and the Dow Jones Industrial Average (DJIA), adopted by 30 prominent companies
 listed in stock markets in the US. The NYSE is open from 9:30 a.m. to 4.00 p.m. local
 time, i.e., from 3:00 p.m. to 10:00 p.m. in the Czech Republic. NYSE markets observe US
 holidays, during which the exchange is closed.
 Figure 1 presents the data distribution in three diverse histograms covering the period
 from 1 August 2020 to 29 December 2022. The histogram in gray represents the distribution
 based on level data; the blue is based on the logarithmic series; and the logarithmic return
 series is in red. The predictions are based on three types (level, log, and log return), while
 only level 1 is presented in the results section. However, estimated predictions with log
 and log return series are available on request. As can be seen from Figure 1, the distribution
 of data improves by moving from level to log and from log to log return. The series has
 the same number of observations, 5706, but differs in outliers. Over 58 data points were
 missing, but this problem has been solved through data interpolation.

predictions with log and log return series are available on request. As can be seen from
 Figure 1, the distribution of data improves by moving from level to log and from log to
 log return. The series has the same number of observations, 5706, but differs in outliers.
 Forecasting 2023, 5 Over 58 data points were missing, but this problem has been solved through data377 inter-
 polation.

 Figure 1. Histogram
 Figure 1. Histogramdistribution
 distributionwith
 withlevel, log,
 level, and
 log, loglog
 and return series.
 return Source:
 series. authors’
 Source: elaboration,
 authors’ elabora-
 based on R studio.
 tion, based on R studio.

 The descriptive statistics Table 1 in the Appendix shows the skewness, kurtosis, the
 The descriptive statistics Table 1 in the Appendix shows the skewness, kurtosis, the
 Jarque–Bera test, the minimum, the maximum and the number of observations. As can be
 Jarque–Bera test, the minimum, the maximum and the number of observations. As can be
 seen from the skewness, kurtosis and the Jarque–Bera test, our data do not hold a normal
 seen from the
 distribution. skewness,
 However, thiskurtosis
 is quite and the for
 natural Jarque–Bera test,
 a time series oura data
 with dailydo not hold a normal
 frequency.
 distribution. However, this is quite natural for a time series with a daily frequency.
 Table 1. Descriptive statistics, based on level, log and log return series.
 Table 1. Descriptive statistics, based on level, log and log return series.
 Type n Mean Median Std Skew Kurtosis Min Max JB
 Type n Mean Median Std Skew Kurtosis Min Max JB
 BCO (Level) 5607 1070.8 1204.3 511.37 −0.15 −1.21 255.1 2051 0.000
BCO (Level) 5607 1070.8 1204.3 511.37 −0.15 −1.21 255.1 2051 0.000
 BCO (Log)
BCO (Log) 5607 5607
 6.82 6.82
 7.09 7.09
 0.61 0.61 −0.74−0.74 −0.84−0.84 5.54
 5.54 7.63
 7.63 0.000
 0.000
 BCO (Log
BCO (Log Return) 5607 0.00 0.00 0.01 0.29 5.42 −0.1 0.09 0.000
 5607 0.00 0.00
 Source: authors. 0.01 0.29 5.42 −0.1 0.09 0.000
Return)
 Source: authors.
 We use Statistica 13 software from TIBECO for data handling, applying linear regres-
 sion and neural networks. The linear analysis involves a sample including the following
 We use Statistica 13 software from TIBECO for data handling, applying linear regres-
 functions: linear, polynomial, logarithmic, exponential, weighted polynomial and poly-
 sion and neural networks. The linear analysis involves a sample including the following
 nomial negative exponential smoothing. First, we calculate the correlation coefficient, i.e.,
 functions: linear, polynomial, logarithmic, exponential, weighted polynomial and poly-
 the dependence of oil and gas prices on time. Regression neural structures will allow
 nomial
 for negative
 a 0.95% exponential
 confidence smoothing.
 interval, generatingFirst, we calculate
 the multilayer the correlation
 perceptron (MLP) coefficient,
 and radial i.e.,
 the dependence
 basis of oil
 function (RBF) and gas prices
 networks. on time. Regression
 The calculations neural
 comprise 5805 structures
 data, will allow
 where time is an for
 independent variable and the commodity price a dependent variable. Figures 2 and 3basis
 a 0.95% confidence interval, generating the multilayer perceptron (MLP) and radial
 function (RBF)
 illustrate networks.
 the MLP and RBFThe calculations
 neural networks.comprise 5805 data, where time is an independ-
 ent variable and the commodity price a dependent variable. Figures 2 and 3 illustrate the
 MLP and RBF neural networks.

023, 5, FOR PEER REVIEW

 Forecasting 2023, 5 378

 Figure 2. MLP neural networks. Source: [36].
 Figure 2. MLP neural networks. Source: [36].

 Figure 2. MLP neural networks. Source: [36].

 Figure 3. RBF neural networks. Source: [37].
 Figure 3. RBF neural networks. Source: [37].
 The equation for an MPL neural structure is as follows [38]:

 Figure 3. RBF neural
 y( xnetworks.
 →
 ) = σ( ∑ wi xi ) Source: [37].
 n

 The equation for an MPL neural structure is as fo
 i =0

 The equation for an RBF neural structure is as follows [38]:
 
 The equation for an MPL neural structure is
 → → 2
 → kx − ck
 y( x ) = e − (
 b
 )
 ( ⃗ ) = (∑ 
 → → → →
 where x represents the input values, y is the output, c is the center, b is the width, k x − c k
 is the distance calculated according to the Euclidean metric,
 →

 b is the 
 →
 kx−ck ( ⃗ )potential
 internal = =0 (∑
 of the RBF unit, and w is the weight value.
 The equation for an RBF neural structure is as =0
 fo
 The equation for an RBF neural structure is a
 ‖ ⃗ −
 ( ⃗ ) = − (

Forecasting 2023, 5 379

 The time series comprises three categories: testing, training and validation. The train-
 ing class involves 70% of the data and generates neural structures, while the rest contain
 15% in each. Both groups measure the reliability of the detected neural model. The calcula-
 tion covers 1000 neural networks, preserving the top 10. The hidden layer of multilayer
 perceptron networks contains 2 to 20 neurons, whereas the hidden layer of the RFB includes
 10 to 30 neurons, which is the outer limit. The hidden and output MLP layers combine
 linear, logistic, hyperbolic tangent, exponential and sinus functions, leaving other settings
 at their defaults (within automatic network creation tools). The method of least squares will
 be used to calculate the neural networks. The mesh generation will be terminated if there is
 no improvement, i.e., a decrease in the value of the square aggregate. Only those neuron
 structures whose respective squared aggregates of residuals are the lowest possible relative
 to the actual gold development will be preserved. The Broyden–Fletcher–Goldfarb–Shanno
 (BFGS) algorithm is also used. It is a local optimization algorithm that adapts machine-
 learning algorithms, such as the logistic regression algorithm. Delays in the time series will
 not be considered, because of the need for extensive calculations and the need to perform
 an additional experiment afterward. Table 2 presents relevant formulae.

 Table 2. Activation function of hidden and output layers of MLP and RBF.

 Function Definition Range
 Identity a (−∞, +∞)
 Logistic sigmoid 1 (0, 1)
 1 + e−a
 Hyperbolic tangent e − e−a
 a
 (−1, +1)
 ea + e − a
 Exponential e−a (0, +∞)
 Sine sin (a) [0, 1]
 Source: [39].

 The error function comprises the least squares, as follows:

 N
 1
 ESOS =
 2N ∑ ( y i − t i )2
 i =1

 where N represents the number of trained cases, yi predicts the target variable, and ti is the
 target variable of the ith case.
 We create a neural network to answer RQ1, predicting the price for the following
 month. The validation covers 20 consecutive trading days, including time series for
 exploring the existing and predicted values within the period. Answering RQ1 determines
 whether the oil price movement depends on economic development. The validation reveals
 the difference (residuals) between the evident price and the forecast price, indicating the
 top network to implement in practice. The best structure is always the one with predicted
 and existing values close to zero.
 RQ2 covers the time series from 2000 to 2022, assessing whether the COVID-19 pan-
 demic harmed commodity price movement. We include 5805 values, calculating the
 arithmetic mean for creating the time series by using a mean function in Excel. The mode
 and median function in Excel provide median and mean values. The minimum and maxi-
 mum oil prices and dispersion measure the distance between the points. We use milestones
 during the COVID-19 pandemic, including the onset, growth and repercussions such as
 lockdowns. A graph illustrates the detected correlations between these events and oil price
 movement, providing calculations and visualizations of the findings.

Forecasting 2023, 5 380

 4. Results
 Table 3 presents the top 10 neural networks from 1000 generated structures.

 Table 3. Summary of active networks (oil—daily data from 2000 to 2022).

 Training Validation Training Error Hidden Output
 Index Net. Name Test Error
 Error Error Algorithm Function Activation Activation
 1 MLP 1-13-1 20.03877 18.92097 21.70152 BFGS 735 SOS Tanh Sine
 2 MLP 1-14-1 18.08013 18.38972 20.96396 BFGS 596 SOS Logistic Identity
 3 MLP 1-18-1 19.48483 19.02263 21.81718 BFGS 918 SOS Logistic Sine
 4 MLP 1-17-1 19.51369 19.09565 22.28044 BFGS 1312 SOS Logistic Sine
 5 MLP 1-18-1 19.07577 17.72344 20.75263 BFGS 8505 SOS Logistic Exponential
 6 MLP 1-14-1 18.86865 18.02551 20.75844 BFGS 5198 SOS Logistic Tanh
 7 MLP 1-17-1 19.27102 18.25229 20.93904 BFGS 9999 SOS Logistic Exponential
 8 MLP 1-14-1 20.25959 18.84478 21.82503 BFGS 9999 SOS Tanh Logistic
 9 MLP 1-13-1 19.40942 21.08859 23.08233 BFGS 283 SOS Tanh Exponential
 10 MLP 1-18-1 16.82161 16.05422 19.36678 BFGS 904 SOS Logistic Logistic
 Source: authors.

 All preserved networks are MLPs, largely outplaying the underperforming and biased
 RBFs. The top 10 structures contained 13 to 20 neurons in the hidden layer and were
 generated by the variant BFGS (Broyden–Fletcher–Goldfarb–Shanno) training algorithm.
 A hyperbolic tangent and logistic sigmoid activated hidden neural layers, whereas five
 functions initiated the output, including sine, identity, exponential, hyperbolic tangent and
 logistic. Table 4 illustrates the correlation coefficient determining the performance of the
 preserved structures in all the data sets.

 Table 4. Correlation coefficients (oil—daily data from 2000 to 2022).

 Network Train Test Validation
 1 MLP 1-13-1 0.977013 0.978338 0.974803
 2 MLP 1-14-1 0.979275 0.978936 0.975573
 3 MLP 1-18-1 0.977647 0.978204 0.974569
 4 MLP 1-17-1 0.977613 0.978108 0.974041
 5 MLP 1-18-1 0.978121 0.979737 0.975867
 6 MLP 1-14-1 0.978361 0.979375 0.975863
 7 MLP 1-17-1 0.977895 0.979126 0.975575
 8 MLP 1-14-1 0.976747 0.978452 0.974627
 9 MLP 1-13-1 0.977746 0.975819 0.973097
 10 MLP 1-18-1 0.980733 0.981667 0.977439
 Source: authors.

Forecasting 2023, 5 381

 The correlation coefficient should equal 1 when looking for the corresponding network.
 All three data sets performed the same, indicating valid structures in the training group,
 validated by the other two sets. Neural networks must show a minimum error rate in all
 three groups. According to Table 4,the correlation coefficients of all the neural structures
 and data sets exceed 0.973, suggesting minimal differences between the networks. Table 5
 then presents the statistical analysis for predictions.

 Table 5. Predictions statistics (oil—daily data from 2000–2022).

 Statistics 1 MLP 2 MLP 3 MLP 4 MLP 5 MLP 6 MLP 7 MLP 8 MLP 9 MLP 10 MLP
 1-13-1 1-14-1 1-18-1 1-17-1 1-18-1 1-14-1 1-17-1 1-14-1 1-13-1 1-18-1
 Minimum prediction
 26.3905 26.1152 25.5647 20.2299 24.4610 27.0507 26.5083 25.9120 24.8399 25.8734
 (Train)
 Maximum prediction
 130.0736 133.2628 129.0131 127.8012 137.3579 124.6570 132.8783 127.9347 134.1820 131.0164
 (Train)
 Minimum prediction
 26.3905 26.1234 25.5649 22.3235 24.4615 27.0507 26.5083 25.9160 24.8402 25.8734
 (Test)
 Maximum prediction
 129.9874 133.0829 128.9972 127.7984 135.9908 124.6420 132.7024 127.8371 134.0083 130.9436
 (Test)
 Minimum prediction
 26.3905 26.1193 25.5647 21.5489 24.4613 27.0507 26.5084 25.9140 24.8400 25.8745
 (Validation)
 Maximum prediction
 130.0663 133.2565 128.3634 126.9342 137.1561 123.8298 132.8783 127.9357 134.1763 131.0035
 (Validation)
 Source: authors.

 Table 4 presents the prediction statistics with residuals. They should be close to zero,
 indicating corresponding values of the input and predicted data. We can also see some
FOR PEER REVIEW 8
 residuals in these networks, containing slight inaccuracies. Figure 4 depicts all the networks
 and the actual price movement, including these values. We provide only a part of the table,
 enclosing the rest in the attachments. Figure 4 demonstrates oil price movement.

 160
 150
 Europe Brent Spot Price FOB (Dollars per Barrel)

 140
 130
 120
 110
 100
 90
 (Output)

 80
 70
 60
 50 Europe Brent Spot Price FOB
 (Dollars per
 40 Barrel)[1.MLP 1-19-1]
 30 [2.MLP 1-20-1]
 20 [3.MLP 1-17-1]
 10 [4.MLP 1-15-1]
 [5.MLP 1-19-1]
 0 [6.MLP 1-17-1]
 -10 [7.MLP 1-18-1]
 -1000 0 1000 2000 3000 4000 5000 6000 [8.MLP 1-18-1]
 -500 500 1500 2500 3500 4500 5500 6500 [9.MLP 1-17-1]
 Case number [10.MLP 1-13-1]

 Figure 4. OilSource:
 Figure 4. Oil price movement. price movement.
 authors.Source: authors.

 The figure proposes that all neural networks performed reasonably well in tracking
 actual oil price movement. Colored curves represent 10 preserved structures, yet they can-
 not indicate the local minimum and maximum variations. Even though the networks have
 very high performance levels, according to the correlation coefficients, they encounter a
 problem when predicting price fluctuations (lowest and highest points). For example, the

Forecasting 2023, 5 382

 The figure proposes that all neural networks performed reasonably well in tracking
 actual oil price movement. Colored curves represent 10 preserved structures, yet they
 cannot indicate the local minimum and maximum variations. Even though the networks
 have very high performance levels, according to the correlation coefficients, they encounter
 a problem when predicting price fluctuations (lowest and highest points). For example, the
 value of 2100 skyrocketed. This is because the global financial crisis started in 2008, and
 the price of oil rapidly rose. The value in a horizontal axis (case number) is expressed by
 the number of observations (detailed input data, in days). Within a few years, the price of
 oil again sharply fell as the financial crisis was still lingering, and there was not as much
 money to trade in oil. It can be seen that from the value of 2400, the price of oil rose to the
 value of 2800, where it stagnated until it reached a value of 3700, where again the price
 of oil rose to the value of 4100 and then rose again until it reached a value of 5200. At
 this point, oil prices hit a trough without networks’ noticing the slump. This case marks
 the onset of the COVID-19 pandemic, witnessing a global social and business lockdown.
 However, why none of the networks could track the alarming situation remains a mystery.
 Despite this inconvenience, all the networks are applicable in practice. In 2022, the price of
 oil again sharply rose, because in February 2022, war broke out in Ukraine. Except for the
 fluctuation at the value of 5200, when the neural networks could not record this extreme,
 the neural network more successfully captured the last changes. After training the neural
 structures, we predicted oil price movement for 20 consecutive days, depicted in Table 6.

 Table 6. Oil price predictions for November 2022.

 Date 1 MLP 2 MLP 3 MLP 4 MLP 5 MLP 6 MLP 7 MLP 8 MLP 9 MLP 10 MLP
 1-13-1 1-14-1 1-18-1 1-17-1 1-18-1 1-14-1 1-17-1 1-14-1 1-13-1 1-18-1
 8 November 2022 91.81 95.15 109.08 100.23 94.81 101.25 72.60 96.94 87.82 90.65
 9 November 2022 91.77 94.74 109.20 100.07 95.62 103.68 70.91 99.16 87.11 90.86
 10 November 2022 91.76 94.60 109.24 100.02 95.92 104.52 70.34 99.97 86.87 90.95
 11 November 2022 91.76 94.48 109.29 99.97 96.22 105.38 69.79 100.81 86.63 91.04
 14 November 2022 91.75 94.32 109.32 99.92 96.53 106.25 69.21 101.69 86.38 91.14
 15 November 2022 91.75 94.17 109.37 99.87 96.86 107.13 68.65 102.60 86.14 91.24
 16 November 2022 91.77 93.74 109.49 99.71 97.90 109.82 66.95 105.53 85.41 91.60
 17 November 2022 91.78 93.60 109.52 99.65 98.27 110.73 66.38 106.57 85.16 91.74
 18 November 2022 91.76 93.44 109.57 99.60 98.65 111.65 65.81 107.64 84.92 91.89
 21 November 2022 91.81 93.30 109.61 99.54 99.04 112.57 65.25 108.73 84.67 92.03
 22 November 2022 91.83 93.15 109.65 99.49 99.44 113.49 64.68 109.85 84.43 92.19
 23 November 2022 91.90 92.70 109.77 99.32 100.72 116.25 62.99 113.34 83.69 92.70
 24 November 2022 91.93 92.54 109.81 99.26 101.17 117.16 62.42 114.54 83.43 92.89
 25 November 2022 91.97 92.39 109.85 99.20 101.64 118.07 61.86 115.75 83.18 93.08
 28 November 2022 92.00 92.23 109.89 99.14 102.11 118.98 61.30 116.98 82.93 93.28
 29 November 2022 92.04 92.08 109.93 99.08 102.60 119.88 60.74 118.20 82.68 93.50
 30 November 2022 92.17 91.60 110.05 98.90 104.14 122.50 59.06 121.88 81.93 94.16
 1 December 2022 92.22 91.44 110.09 98.85 104.68 123.35 58.50 123.10 81.68 94.4
 2 December 2022 92.28 9129 110.13 98.78 105.23 124.19 57.95 124.30 81.42 94.64
 5 December 2022 92.33 91.12 110.17 98.72 105.79 125.01 57.39 125.48 81.17 94.89
 Source: authors.

Forecasting 2023, 5 383

 Table 6 depicts oil price movement from 8 November 2022 to 5 December 2022. The
 first two networks show a price range from 91.75 to 95.15. On the other hand, from the
 third structure, we see an inconsistent rise and fall. Strangely enough, the sixth and eighth
 networks mark price hikes in November, while the seventh model indicates a slump below
 the level of other neural networks, which do not drop under 81.42. Table 7 illustrates actual
 oil price movement for November 2022.

 Table 7. Actual oil price movement.

 Date Real Price of Oil
 8 November 2022 96.85
 9 November 2022 93.05
 10 November 2022 94.25
 11 November 2022 96.37
 14 November 2022 93.59
 15 November 2022 94.30
 16 November 2022 92.61
 17 November 2022 91.00
 18 November 2022 88.93
 21 November 2022 88.44
 22 November 2022 88.65
 23 November 2022 85.90
 24 November 2022 85.59
 25 November 2022 83.40
 28 November 2022 83.50
 29 November 2022 83.22
 30 November 2022 85.61
 1 December 2022 86.28
 2 December 2022 86.54
 5 December 2022 83.36
 Source: authors.

 We can see that the actual oil price was much lower than what some neural networks
 predicted. At the beginning of November, the price topped USD 96.85 per barrel, witnessing
 a steady decline until 30 November 2022. At that time, the values again increased until 5
 December and then plummeted to the rates before 30 November.
 Table 8 presents the differences between real oil prices and predictions of oil prices.

Forecasting 2023, 5 384

 Table 8. Differences between real oil prices and predictions.

 Residuals Residuals Residuals Residuals Residuals Residuals Residuals Residuals Residuals Residuals
 Date 1 MLP 2 MLP 3 MLP 4 MLP 5 MLP 6 MLP 7 MLP 8 MLP 9 MLP 10 MLP
 1-13-1 1-14-1 1-18-1 1-17-1 1-18-1 1-14-1 1-17-1 1-14-1 1-13-1 1-18-1
 8 November 2022 5.04 1.70 −12.23 −3.38 2.04 −4.40 24.25 −0.09 9.03 6.20
 9 November 2022 1.28 −1.69 −16.15 −7.02 −2.57 −10.63 22.14 −6.11 5.94 2.19
 10 November 2022 2.49 −0.35 −14.99 −5.77 −1.67 −10.27 23.91 −5.72 7.38 3.30
 11 November 2022 4.61 1.89 −12.92 −3.60 0.15 −9.01 26.58 −4.44 9.74 5.33
 14 November 2022 1.84 −0.73 −15.73 −6.33 −2.94 −12.66 24.38 −8.10 7.21 2.45
 15 November 2022 2.55 0.13 −15.07 −5.57 −2.56 −12.83 25.65 −8.30 8.16 3.06
 16 November 2022 0.84 −1.13 −16.88 −7.10 −5.29 −17.21 25.66 −12.92 7.20 1.01
 17 November 2022 −0.78 −2.60 −18.52 −8.65 −7.27 −19.73 24.62 −15.57 5.84 −0.74
 18 November 2022 −2.83 −4.51 −20.64 −10.67 −9.72 −22.72 23.12 −18.71 4.01 −2.96
 21 November 2022 −3.37 −4.86 −21.17 −11.10 −10.60 −24.13 23.19 −20.29 3.77 −3.59
 22 November 2022 −3.18 −4.50 −21.00 −10.84 −10.79 −24.84 23.97 −21.20 4.22 −3.54
 23 November 2022 −6.00 −6.80 −23.87 −13.42 −14.82 −30.35 22.91 −27.44 2.21 −6.80
 24 November 2022 −6.34 −6.95 −24.22 −13.67 −15.58 −31.57 23.17 −28.95 2.16 −7.30
 25 November 2022 −8.57 −8.99 −26.45 −15.80 −18.24 −34.67 21.54 −32.35 0.22 −9.68
 28 November 2022 −8.50 −8.73 −26.39 −15.64 −18.61 −35.48 22.20 −33.48 0.57 −9.78
 29 November 2022 −8.82 −8.86 −26.71 −15.86 −19.38 −36.66 22.48 −34.98 0.54 −10.28
 30 November 2022 −6.56 −5.99 −24.44 −13.29 −18.53 −36.89 26.55 −36.27 3.68 −8.55
 1 December 2022 −5.94 −5.16 −23.81 −12.57 −18.40 −37.07 27.78 −36.82 4.60 −8.12
 2 December 2022 −5.74 −4.75 −23.59 −12.24 −18.69 −37.65 28.59 −37.76 5.12 −8.10
 5 December 2022 −8.97 −7.76 −26.81 −15.36 −22.43 −41.65 25.97 −42.12 2.19 −11.53
 Total −56.96 −80.64 −411.59 −207.88 −215.90 −490.42 488.66 −431.62 93.79 −67.43
 Mean −2.85 −4.03 −20.58 −10.39 −10.8 −24.52 24.43 −21.58 4.69 −3.37
 Median −3.28 −4.63 −21.09 −10.97 −10.7 −24.49 24.11 −20.75 4.41 −3.57
 Source: authors.

 We can see that the first neural network, whose total value, mean and median are the
 closest to zero, closely mimicking reality, shows the best results. On the other hand, the
 sixth neural network performed the worst, indicating the highest dispersion, forecasting
 much higher oil prices. The seventh neural structure did not perform well, either, setting
 the price too low compared to the actual situation. Table 8 also shows that the predicted
 price was close to reality on the 8th, 11th and 15th of November. Most residuals are minus,
 demonstrating huge differences between the predicted data and the actual data. This issue
 can also be looked at in the form of trend monitoring. Although some prediction networks
 showed very different values from the actual value, they successfully followed the trend
 of natural development (more or less similar decline and growth). This can be seen, for
 example, in the seventh MLP 1-17-1 network if we compare the predicted values, in Table 6,
 and the actual values, in Table 7.
 Figure 5 illustrates the price difference between gasoline and oil.

R PEER REVIEW
 Forecasting 2023, 5 385

 Figure 5. Price
 Figure 5. Price differences differencesoil
 between between
 and oil and gasoline.
 gasoline. Source: authors.
 Source: authors.

 The extreme variations indicate that oil prices wildly fluctuated during the monitored
 The extreme period comparedindicate
 variations with gasoline
 thatprices. Figure 5wildly
 oil prices proposesfluctuated
 that 2008 and 2009
 during saw athe
 pricemonito
 hike after the Great Recession, followed by a sharp drop in 2009. Despite the ongoing
 period compared withcrisis,
 financial gasoline prices.
 global markets Figure
 found a way to5push
 proposes
 oil prices that 2008
 up again, and in2009
 as shown Figuresaw
 5. ap
 hike after the Great
 The nextRecession, followed
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 2020, sharp thedrop
 COVID-19 in 2009.
 pandemic Despite
 inhibitedthe
 the ongo
 global economy with massive lockdowns until 2021. It can be seen from Figure 5 that
 financial crisis, global markets found a way to push oil prices up again, as shown in Fig
 there was a massive drop in the price of oil at this time: before the onset of the COVID-19
 5. The next economic
 pandemic,upheaval
 the cost ofcame in 2020,
 oil hovered aroundwhen
 USD 63the COVID-19
 per barrel, and at thepandemic
 beginning ofinhibited
 the
 global economypandemic (i.e., sometime around 1 January 2020), the price of oil fell only slightly, to USD
 with massive lockdowns until 2021. It can be seen from Figure 5 that th
 59 per barrel. The big jump happened around 22 July 2020, when the price of oil had fallen
 was a massive dropto USDin9 per
 thebarrel.
 priceAsofofoil at this
 August 2020,time:
 the costbefore thestarted
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 In 2022, the p
 demic, the cost ofwaroil
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 hovered again dramatically
 around USD drove
 63 oil
 perprices up, yet
 barrel, leaving
 and gasoline
 at the prices intact.
 beginning of the p
 What causes the wild fluctuation of fuels? Gasoline reflects oil prices, including high taxes
 demic (i.e., sometime around
 (excise duty and GNP)1 January
 and refinery2020),
 marginsthethat price
 increaseoftheoil fell
 limit onlyduring
 10 times slightly,
 a crisis.to USD
 per barrel. The big jump happened
 The Russia–Ukraine War alsoaround 22toJuly
 contributes 2020,
 high fuel when
 prices, thetheprice
 because US and oftheoil
 EUhad fa
 banned oil imports from Russia, relying heavily on shippers from other countries.
 to USD 9 per barrel. As of August 2020, the cost of oil again started to rise. In 2022, the w
 in Ukraine again5. dramatically
 Discussion drove oil prices up, yet leaving gasoline prices intact. W
 This work explored oil price movement in stock markets and the extent that they
 causes the wild fluctuation of fuels? Gasoline reflects oil prices, including high taxes
 suffered from the COVID-19 pandemic. The data analysis covered the years 2000 to 2022,
 cise duty and GNP) and
 including refinery
 5805 margins
 items processed that increase
 in Statistica 13 software.the limit
 Recent 10 have
 years timesseenduring
 much a cr
 research on commodity price movement, using artificial
 The Russia–Ukraine War also contributes to high fuel prices, because the US andneural networks calculated in the
 Statistica and Matlab. Vochozka, Horák and Krulicky [28] listed the most common software
 banned oil imports
 tools,from Russia,
 including relying
 JavaScript, Python,heavily
 Tensor Flow onand
 shippers
 Matlab. from other countries.
 Naderi, Khamehchi and Karimi [40] applied neural structures to predict monthly
 oil prices, daily gas prices and annual interest rates. Their findings revealed that their
 5. Discussion method reduces the mean squared error by at least 6.61% in the monthly oil price, 18.33%
 This work inexplored
 the daily gasoil
 price and 23.13%
 price in the annual
 movement in interest
 stockrate prognosisand
 markets compared
 thewith other that t
 extent
 forecasting techniques.
 suffered from the COVID-19 pandemic.
 The research questions of thisThe
 studydata analysis
 were as follows: covered the years 2000 to 20
 including 5805 items processed in Statistica 13 software. Recent years have seen m
 research on commodity price movement, using artificial neural networks calculated
 Statistica and Matlab. Vochozka, Horák and Krulicky [28] listed the most common s
 ware tools, including JavaScript, Python, Tensor Flow and Matlab.

Forecasting 2023, 5 386

 RQ1: What will be the oil and gas prices on the commodity market in November 2022?
 Answering RQ1 involved a neural network predicting commodity prices for the
 following month, revealing that November 2022 saw oil prices between USD 91.75 and
 USD 125.48 per barrel. The first two neural structures showed price movement between
 USD 91.75 and USD 95.15, while the values of the rest fluctuated. Strangely enough,
 the sixth and eighth networks indicated a sharp price hike during November, while the
 seventh network indicated much lower values than the other neural networks, which never
 dropped below USD 81.42. The oil price will then be on the rise. We generated 1000 neural
 models, preserving the top 10. All of them were MLP models, including 13–20 neurons in
 the hidden layer and trained by variants of the BFGS (Broyden–Fletcher–Goldfarb–Shanno)
 algorithm. The correlation coefficients of all the networks and data sets were higher than
 0.973, showing only minimal differences.
 RQ2: What was the impact of the COVID-19 pandemic on oil stock prices?
 RQ2 comprised a time series from 2000 to 2022, measuring the impact of the COVID-19
 pandemic on oil price movement and a potential slump in commodity prices. We found
 that the pandemic was the main driving force behind the oil rates. Although the onset
 did not damage the market much, consequent lockdowns severely inhibited the economy,
 driving oil prices down. The rates did not begin to rise until 2021.
 We also explored fuel prices at petrol stations, assessing whether they were due to
 inflation or to distributors’ seizing the opportunity to boost profits. Because oil prices have
 incurred violent fluctuations over the past two decades while gasoline has commanded
 the same market price, it is evident that distributors only seized an opportunity in the
 calamity. The gas reflects oil rates, including high taxes (excise duty and GNP), and refinery
 margins increased 10 times when expecting or experiencing a crisis. Another contributor
 to exorbitant fuel prices is the ongoing war in Ukraine, as the US and the EU banned oil
 imports from Russia, looking for supplies from elsewhere.

 6. Conclusions
 Predicting commodity prices is essential for developing effective strategies for effi-
 ciently handling stock market transactions. All the people involved in the stock exchange
 follow forecasts of price movements, including shareholders, traders and companies. Oil
 prices also draw in the public, as this resource concerns our daily lives. Predicting com-
 modity prices is essential for developing effective strategies for efficiently handling stock
 market transactions. All the people involved in the stock exchange follow forecasts of price
 movements, including shareholders, traders and companies.
 The present study aimed to predict oil price movement in stock markets, assessing the
 impact of the COVID-19 pandemic. We found that oil deeply upset gasoline prices, closely
 reflecting the economic (the pandemic, inflation) or political situation in neighboring countries.
 If Europe or the world faces a war or a pandemic, commodity prices (oil) soar, and they
 are highly susceptible to supply and demand and deeply suffer from economic plights. The
 correlation coefficients of all the neural networks and data sets exceeded 0.973, indicating
 only minimal differences. Another partial goal was to find out the price at which fuel is
 sold at gas stations and assess whether it is necessary to raise the price or whether it is a
 classic move by distributors to use the situation to their advantage and increase profits. It
 was found that this is a classic move by distributors, as the price of benzene has hardly
 moved over the past 20 years, while the price of oil, on the other hand, has had a very
 fluctuating tendency. However, we also have to consider that tax is included in the price of
 gasoline, and the margin of refineries is also included here, which can increase this margin
 even 10 times when a crisis period is expected or a crisis period is currently underway.
 Another reason fuel prices are so high now is the ongoing war in Ukraine, as the US and
 the EU have banned the oil supply from Russia, so there is pressure on the oil supply from
 other countries.
 We also revealed that all neural networks performed well in tracking actual oil price
 movement, although some undetected fluctuations occurred over the monitored period.

Forecasting 2023, 5 387

 Despite these setbacks, all the models are applicable in practice. Once trained, the networks
 predicted oil price movement for 20 trading days. The total correlation coefficients showed
 that the 10th MLP 1-18-1 network was the best to apply in practice. The seventh neural
 network was the best at predicting the trend following the development of the actual
 value, but the residual was the worst. The residual at the seventh neural network came out
 USD 20 lower, but it managed the trend the best despite that.
 However, the coefficients are so close, almost identical, that we cannot satisfactorily
 say which network is the best. All the networks need further training to yield results that
 are more accurate. Validation showed that the first model was closest to zero and, thereby,
 the most reliable to train on extensive data to achieve higher accuracy. Although all the
 networks can somehow predict oil price movement, they are still too far from reality to be
 suitable in practice.
 Oil prices were calculated using the least squares method. Time series lags were
 not considered, because of because of the need for extensive calculations and the need to
 perform additional experiments afterward. This should be the subject of ongoing research.
 According to the correlation coefficients, the networks are of high quality and perform well,
 but when the residuals are added up, it is found that they are not so good, as the networks
 can smooth the historical time series of oil prices very well but are less useful at providing
 accurate predictions, especially for a more-extended period.
 The study is limited by involving only a few neural networks. Our research also lacked
 a comparison with other commodities, as we explored only oil prices. The survey will
 continue by validating the oil price for December 2022. Furthermore, it would be helpful
 to solve another analysis on the development of the trend in noniron networks because,
 in most cases, they cannot have the same values as the residuals can. Neural networks
 cannot capture local minima and maxima but can detect a trend. They also cannot capture
 extremes, as they are preset, so it is necessary to take the structures of these preserved
 networks, train them on new ones and improve their predictive abilities.

 Author Contributions: Conceptualization, J.H. and M.J.; methodology, J.H. and M.J.; software, J.H.
 and M.J.; validation, J.H.; formal analysis, M.J.; investigation, J.H.; resources, M.J.; data curation, J.H.
 and M.J.; writing—original draft preparation, M.J.; writing—review and editing, J.H.; visualization,
 M.J.; supervision, J.H. All authors have read and agreed to the published version of the manuscript.
 Funding: This research was supported/funded by IVSUZO2301—The impact of the circular economy
 on the share prices of companies listed on the stock exchange.
 Institutional Review Board Statement: Not applicable.
 Informed Consent Statement: Not applicable.
 Data Availability Statement: The data sets used in this contribution were sourced from https://www.
 macrotrends.net/2480/brent-crude-oil-prices-10-year-daily-chart (accessed on 25 November 2022).
 Conflicts of Interest: The authors declare no conflict of interest.

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